The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 2X 0 0 2X 2X 2X 0 0 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 0 0 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 0 0
0 0 2X 0 0 0 0 0 0 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 0
0 0 0 2X 0 0 0 0 0 2X 0 2X 0 2X 0 2X 2X 0 0 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 0 0
0 0 0 0 2X 0 0 0 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 2X 0 2X 0 2X 0 0 0 2X 2X 0 0 0 0 2X 2X 2X 0 2X 0 2X 2X 0 0 2X 0 0 0 2X 2X 0 0 2X 2X 2X 0 0 0
0 0 0 0 0 2X 0 2X 2X 0 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0
0 0 0 0 0 0 2X 2X 0 0 2X 0 2X 2X 0 2X 0 0 2X 2X 0 2X 0 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 0 2X 2X 0 0 0
generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+19x^52+44x^56+896x^58+44x^60+19x^64+1x^116
The gray image is a code over GF(2) with n=464, k=10 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.